Understanding relation between VC Symmetrization Lemma and Generalization Bounds
Let $\varepsilon$ in (17) is equal to $\sqrt{\frac{4}{n}\left(\log{(2\mathsf{N}(\mathcal{F},n))}-\log{\delta}\right)}$. We have:

$$
P\left(\sup_{f\in\mathcal{F}}|R(f)-R_{emp}(f)| &gt; \sqrt{\frac{4}{n}\left(\log{(2\mathcal{N}(\mathcal{F},n))}-\log{\delta}\right)}\right) \leqslant 
2\mathcal{N}(\mathcal{F},n) e^{\frac{-n}{4}\left(\frac{4}{n}\left(\log{(2\mathcal{N}(\mathcal{F},n))}-\log{\delta}\right)\right)} = 
2\mathcal{N}(\mathcal{F},n) e^{\log{\delta} - \log{(2\mathcal{N}(\mathcal{F},n))}}
$$

As we know that $e^{\log{n}} = n$ (suppose that base of $\log$ here is $e$), we can write:

$$
P\left(\sup_{f\in\mathcal{F}}|R(f)-R_{emp}(f)| &gt; \sqrt{\frac{4}{n}\left(\log{(2\mathcal{N}(\mathcal{F},n))}-\log{\delta}\right)}\right) \leqslant 
2\mathcal{N}(\mathcal{F},n) \left(\frac{\delta}{2\mathcal{N}(\mathcal{F},n)}\right)
$$

Hence:

$$
P\left(\sup_{f\in\mathcal{F}}|R(f)-R_{emp}(f)| &gt; \sqrt{\frac{4}{n}\left(\log{(2\mathcal{N}(\mathcal{F},n))}-\log{\delta}\right)}\right) \leqslant \delta
$$
As we know that if we have $P(x &gt; a) \leqslant c$, we can conlude that $P( x&lt;a) \geqslant 1-c$, we will have:

$$
P\left(\sup_{f\in\mathcal{F}}|R(f)-R_{emp}(f)| &lt; \sqrt{\frac{4}{n}\left(\log{(2\mathcal{N}(\mathcal{F},n))}-\log{\delta}\right)}\right) \geqslant 1- \delta
$$

Now, as this inequality is true for supremum of set $\mathcal{F}$ and $R(f) -R_{emp}(f) \leqslant \varepsilon$ is subset of  $|R(f) -R_{emp}(f)| \leqslant \varepsilon$ (in terms of probability state space), we can say the following inequality is correct for any function $f$ with at least probability of $1-\delta$:
$$
R(f) \leqslant R_{emp}(f) + \sqrt{\frac{4}{n}\left(\log{(2\mathcal{N}(\mathcal{F},n))}-\log{\delta}\right)}
$$